With significant progress of information and communication technologies in recent years involving electronic trading and e-mail, cryptographic technologies applicable to transmission of information have been studied vigorously. As one of such cryptographic technologies, quantum cryptography is drawing attention.
The safety of quantum cryptography is ensured by physical phenomena according to Heisenberg's uncertainty principle in quantum mechanics. According to the uncertainty principle, since quantum state changes by the eavesdropping of communication, namely observation, becomes apparent without fail, and necessary measures including interruption of communication can be implemented accordingly. The eavesdropping is therefore regarded physically impossible. Reproduction of particles is also deemed impossible according to the uncertainty principle.
Quantum teleportation is a major element of quantum cryptography. Quantum teleportation is a technique of transporting quantum information of particles only to other places. Quantum teleportation is achieved by allowing photons to exchange information using quantum entanglement. A photon pair has characteristics that once the quantum state of one of the pair in an entangled state is determined, the quantum state of the other is also determined. The characteristics do not depend on the distance between two photons.
With the quantum teleportation technology described above, a pair of photons in a state of quantum entanglement is absolute imperative. Various methods of generating photon pairs in a state of quantum entanglement are known. For example, Patent Reference 1 discloses irradiating two parent photons to a semiconducting material to generate an exciton molecule whose angular momentum is 0 by two-photon resonant excitation, and simultaneously splitting the generated exciton molecule into two photons, thus generating a photon pair in a state of quantum entanglement.
Quantum entanglement achieved by polarized light of two photons is also used. As a state of quantum entanglement of two quantum bits (two photons) using polarized light, four conditions expressed by the following equations (1) and (2) are known.
                                                                    Ψ              ±                        〉                    12                ≡                              1                          2                                ⁢                      (                                                                                                    H                    〉                                    1                                ⁢                                                                          V                    〉                                    2                                            ±                                                                                        V                    〉                                    1                                ⁢                                                                          H                    〉                                    2                                                      )                                              (        1        )                                                                                Φ              ±                        〉                    12                ≡                              1                          2                                ⁢                      (                                                                                                    H                    〉                                    1                                ⁢                                                                          H                    〉                                    2                                            ±                                                                                        V                    〉                                    1                                ⁢                                                                          V                    〉                                    2                                                      )                                              (        2        )            
where, |H>i represents that a photon having a first polarized light (H) exists in mode i (i: 1 or 2), and |V>i represents that a photon having a second polarized light (V) exists in mode i′ (i′: 1 or 2). As physical quantity determining the modes of photons i, i′, optical paths and angular frequency of photons are considered.
(Method of Generating a Two-Photon State Using Parametric Down-Conversion)
As a physical process of generating a two-photon state, process of spontaneous parametric down-conversion is used frequently. In the process of spontaneous parametric down-conversion, a pumping photon having an angular frequency ωp and wave vector kp that has entered a nonlinear optical crystal is converted at a certain probability into a photon pair of signal photon having angular frequency ωs and wave vector ks and idler photon having angular frequency ωi and wave vector ki. In this case, as phase matching conditions for causing the process of spontaneous parametric down-conversion to occur, the angular frequency condition shown by equation (3) and the momentum conversation law shown by equation (4) must be satisfied at the same time. The angular frequency condition is also called the energy conservation law.ωp=ωs+ωi  (3)kp=ks+ki  (4)
Phase matching conditions are classified into the following three types depending on the polarized light of each photon:
(a) Type 0 Phase Matching Condition
The case where a pumping photon, signal photon, and idler photon have the same polarized light is called type 0 phase matching condition.
(b) Type I Phase Matching Condition
The case where a signal photon and idler photon have the same polarized light, and a pumping photon has a polarization state orthogonal to the signal and idler photons, is called type I phase matching condition.
(c) Type II Phase Matching Condition
The case where the polarized light of a signal photon and that of an idler photon cross orthogonal to each other, and a pumping photon has the polarized light of one of the above-mentioned photons is called type II phase matching condition.
(Method of Achieving High Degree of Polarization Entanglement Using a Wavelength Band-Limiting Filter)
A signal photon and an idler photon generated by the process of spontaneous parametric down-conversion have broadband wavelength spectra. Generally, if a signal photon and an idler photon having broadband wavelength spectra are used, the coherence time of two photons may decrease, thus deteriorating polarization entanglement. To increase the degree of polarization entanglement of generated photon pairs, a method of limiting the spectra of idler photons using a wavelength band-limiting filter is available. An interference filter having a dielectric multilayer structure is generally used to limit wavelength band. This type of interference filter can pass light having a given center wavelength and band width based on structural design, but the wavelength band allowed to be passed at a time is limited to one kind of band. Consequently, conventional methods have focused mainly on generating narrowband parametric photon pairs.
Assuming the speed of light in vacuum as c, the angular frequency ω and wavelength λ of a photon are expressed by equation (5) as shown below. If the angular frequency ω of the photon is defined, the wavelength λ can be found using the following equation. Therefore, the angular frequency and the wavelength are used as approximately the same meaning because angular frequency is easy to handle theoretically, and wavelength is easy to handle experimentally.ω=2πc/λ  (5)
(Conventional Method of Generating a State of Polarization Entanglement)
Some methods of generating a state of polarization entanglement where two photons have the same angular frequency have been reported (Non-Patent Reference 1, for example). With the method disclosed in Non-Patent Reference 1, since the angular frequency of two photons is indistinguishable from each other, the mode is determined by the optical paths of the photons. Namely, the two photons must be emitted into different optical paths.
Meanwhile, a method of generating a state of polarization entanglement where two photons have different angular frequencies has also been proposed. With this method, since the mode of a photon is distinguished from that of the other by their angular frequencies, the two photons can exist on the same optical path.
As a method of generating a state of polarization entanglement where two photons have different angular frequencies, Non-Patent Reference 2 discloses a method of using type 0 or type I parametric down-conversion. Non-Patent Reference 2 generates a photon pair by placing nonlinear optical crystals in series, rotating by 90 degrees from each other, so that type 0 or type I phase matching conditions for generating two photons having the same polarized light state are satisfied. In this case, light from the same pump light source is irradiated to two crystals, and thus two photons (ω1, ω2) having different angular frequencies are generated in the coaxial direction of the pump light. However, this method involves complexity that two crystals having the same characteristics must be provided and arranged accurately.
Non-Patent Reference 4 discloses a method of using type 0 or type I parametric down-conversion and an interferometer. This method generates a photon pair by placing a nonlinear optical crystal in an interferometer so that type 0 or type I phase matching conditions for generating two photons having the same polarized light state are satisfied. However, since this method uses an interferometer, equipment structure becomes complicated.
Non-Patent Reference 5 discloses generation of photon pairs under type 0 phase matching condition.
Patent Reference 2 discloses a method of creating two types of periodically poled structures in a single crystal. Since this method uses different phase matching conditions, namely types 0 and I, it is difficult to balance the generation efficiency of two photons generated in each periodically poled structure that satisfy each phase matching condition, which is a disadvantage. Poor balance in generation efficiency of two photons generated in each periodically poled structure results in decrease in the degree of quantum entanglement.
Non-Patent Reference 3 discloses a method using a four optical wave mixing process, namely a third order nonlinear optical phenomenon that occurs in optical fibers. With this method, since optical fibers must be installed within an interferometer to generate a state of polarization entanglement, equipment configuration becomes complicated.